Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×#10596831 |
| derived, Sylow | C73 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D73 |
| commutator, hypocenter | C73 | C24×C8 |
| Frattini | C4 | C24×D73 |
| Fitting | C24×C4×C73 | C2 |
| socle | C25×C73 | C4 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C24×C4 | |
1976 conjugacy classes of subgroups.
2432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32991207, #32991209, #32991233, … |
| maximal normal subgroup of | #32991207, #32991209, #32991233, … |
| maximal quotient of | C23×C4×#10596831, C23×C22⋊#10596831, C23×C4⋊#10596831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19209);